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Geometric invariant theory/ D. Mumford, J. Fogarty and F. Kirwan

By: Mumford, DContributor(s): Fogarty, J | Kirwan, FMaterial type: Text

TextPublication details: Berlin: Springer-Verlag, c1994Edition: 3rd enl. edDescription: xiv, 292 p. : ill. ; 24 cmISBN: 3540569634Subject(s): Algebraic Geometry | Invariants | Moduli theoryDDC classification: 516.35

Contents:

Preliminaries -- 1. Definitions -- 2. First properties -- 3. Good and bad actions -- 4. Further properties -- 5. Resume of some results of Grothendieck -- Fundamental theorems for the actions of reductive groups -- 1. Definitions -- 2. The affine case -- 3. Linearization of an invertible sheaf -- 4. The general case -- 5. Functional properties -- Analysis of stability -- 1. A numeral criterion -- 2. The flag complex -- 3. Applications -- An elementary example -- 1. Pre-stability -- 2. Stability -- 4. Further examples -- 1. Binary quantics -- 2. Hypersurfaces -- 3. Counter-examples -- 4. Sequences of linear subspaces -- 5. The projective adjoint action -- 6. Space curves -- The problem of moduli -- 1st construction -- 1. General discussion -- 2. Moduli as an orbit space -- 3. First chern classes -- 4. Utilization of 4.6 -- Abelian schemes -- 1. Duals -- 2. Polarizations -- 3. Deformations -- The method of covariants -- 2nd construction -- 1. The technique -- 2. Moduli as an orbit space -- 3. The covariant -- 4. Application to curves -- The moment map -- 1. Symplectic geometry -- 2. Symplectic quotients and geometric invariant theory -- 3. Kahler and hyperkahler quotients -- 4. Singular quotients -- 5. Geometry of the moment map -- 6. The cohomology of quotients: the symplectic case -- 7. The cohomology of quotients: the algebraic case -- 8. Vector bundles and the Yang-Mills functional -- 9. Yang-Mills theory over Riemann surfaces.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	516.35 MUM/G (Browse shelf(Opens below))	Available		P25305

Total holds: 0

Preliminaries --
1. Definitions --
2. First properties --
3. Good and bad actions --
4. Further properties --
5. Resume of some results of Grothendieck --
Fundamental theorems for the actions of reductive groups --
1. Definitions --
2. The affine case --
3. Linearization of an invertible sheaf --
4. The general case --
5. Functional properties --
Analysis of stability --
1. A numeral criterion --
2. The flag complex --
3. Applications --
An elementary example --
1. Pre-stability --
2. Stability --
4. Further examples --
1. Binary quantics --
2. Hypersurfaces --
3. Counter-examples --
4. Sequences of linear subspaces --
5. The projective adjoint action --
6. Space curves --
The problem of moduli --
1st construction --
1. General discussion --
2. Moduli as an orbit space --
3. First chern classes --
4. Utilization of 4.6 --
Abelian schemes --
1. Duals --
2. Polarizations --
3. Deformations --
The method of covariants --
2nd construction --
1. The technique --
2. Moduli as an orbit space --
3. The covariant --
4. Application to curves --
The moment map --
1. Symplectic geometry --
2. Symplectic quotients and geometric invariant theory --
3. Kahler and hyperkahler quotients --
4. Singular quotients --
5. Geometry of the moment map --
6. The cohomology of quotients: the symplectic case --
7. The cohomology of quotients: the algebraic case --
8. Vector bundles and the Yang-Mills functional --
9. Yang-Mills theory over Riemann surfaces.

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